Make "S" the subject of formula in V = sqrt(U2 + 2AS)

Question 1: Step 1: Break down the number 999,999,999,995 into place value groups. The number is 999 billion, 999 million, 999 thousand, and 995. Step 2: Write the number in words based on the place value groups. Nine hundred and ninety-nine billion, nine hundred and ninety-nine million, nine hundred and ninety-nine thousand and ninety-five. The correct option is C. C. Nine hundred and ninety-nine billion, nine hundred and ninety-nine million, nine hundred and ninety-nine thousand and ninety-five Question 2: Step 1: Find the H.C.F (Highest Common Factor) for the first set of numbers: 9, 12, 15, 24. Factors of 9: 1, 3, 9 Factors of 12: 1, 2, 3, 4, 6, 12 Factors of 15: 1, 3, 5, 15 Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 The common factors are 1, 3. The H.C.F is 3. Step 2: Find the H.C.F for the second set of numbers: 9, 12, 15. Factors of 9: 1, 3, 9 Factors of 12: 1, 2, 3, 4, 6, 12 Factors of 15: 1, 3, 5, 15 The common factors are 1, 3. The H.C.F is 3. Step 3: Find the product of the two H.C.F values. Product = 3 × 3 = 9. The correct option is C. C. 9 Question 3: Step 1: Identify the total volume of palm oil and the volume each bottle holds. Total volume = 210 litres. Volume per bottle = (3)/(4) litres. Step 2: Divide the total volume by the volume per bottle to find the number of bottles. Number of bottles = Total volumeVolume per bottle = (210)/(3)4 Step 3: Perform the division. Number of bottles = 210 × (4)/(3) = (210 × 4)/(3) = 70 × 4 = 280 The correct option is B. B. 280 Question 4: Step 1: Find the H.C.F (Highest Common Factor) of 9, 12, and 18. Prime factorization: 9 = 3^2 12 = 2^2 × 3 18 = 2 × 3^2 The common prime factor is 3, and the lowest power is 3^1. So, H.C.F = 3. Step 2: Find the L.C.M (Lowest Common Multiple) of 9, 12, and 18. The prime factors involved are 2 and 3. Highest power of 2 is 2^2. Highest power of 3 is 3^2. L.C.M = 2^2 × 3^2 = 4 × 9 = 36. Step 3: Find the product of the L.C.M and H.C.F. Product = 36 × 3 = 108. The correct option is A. A. 108 Question 5: Step 1: Recognize that the angles 60^, 4x, and 2x lie on a straight line. The sum of angles on a straight line is 180^. Step 2: Set up the equation and solve for x. 60^ + 4x + 2x = 180^ 60^ + 6x = 180^ 6x = 180^ - 60^ 6x = 120^ x = (120^)/(6) x = 20^ The correct option is C. C. 20^ Question 6: Step 1: Visualize the problem as a right-angled triangle. The ladder is the hypotenuse (6m). The angle with the wall is 30^. We need to find the distance of the foot of the ladder from the wall, which is the side opposite to the 30^ angle. Step 2: Use the sine trigonometric ratio. () = oppositehypotenuse (30^) = distance6 Step 3: Solve for the distance. distance = 6 × (30^) Since (30^) = 0.5: distance = 6 × 0.5 = 3.00 m The correct option is C. C. 3.00m Question 7: Step 1: Identify the given dimensions and properties of the trapezoid. Top side (BC) = 8 cm. Bottom side (AD) = 16 cm. Height = 3 cm. Sides AB and CD are equal, indicating an isosceles trapezoid. Step 2: Find the length of the non-parallel sides (AB and CD). Draw perpendiculars from B and C to AD, let them meet AD at E and F respectively. Then BCFE is a rectangle, so EF = 8 cm. Since it's an isosceles trapezoid, AE = FD = AD - EF2 = (16 - 8)/(2) = (8)/(2) = 4 cm. Consider the right-angled triangle ABE. The height BE = 3 cm, AE = 4 cm. Using the Pythagorean theorem: AB^2 = AE^2 + BE^2 AB^2 = 4^2 + 3^2 AB^2 = 16 + 9 AB^2 = 25 AB = sqrt(25) = 5 cm So, CD = 5 cm. Step 3: Calculate the perimeter. Perimeter = AB + BC + CD + AD Perimeter = 5 + 8 + 5 + 16 = 34 cm The correct option is D. D. 34cm Question 8: Step 1: Start with the given formula. V = sqrt(U^2 + 2aS) Step 2: Square both sides to eliminate the square root. V^2 = U^2 + 2aS Step 3: Isolate the term containing S by subtracting U^2 from both sides. V^2 - U^2 = 2aS Step 4: Make S the subject by dividing both sides by 2a. S = (V^2 - U^2)/(2a) The correct option is C. C. S = (V^2 - U^2)/(2a) Drop the next question.